dp : 0.5(qº – q°) dt Where qD = 30 – 2p is the demand function, qs = 2N is the supply function, p is price, N is the number of firms in the industry and a is the speed of adjustment coefficient. The number of firms adjust according to dN (р — 10) %D dt 4 (i) Derive the linear second-order differential equation implied by this model. (ii) Solve the second-order differential equation. (iii) Derive a system of differential equation to represent this information.

dp : 0.5(qº – q°) dt Where qD = 30 – 2p is the demand function, qs = 2N is the supply function, p is price, N is the number of firms in the industry and a is the speed of adjustment coefficient. The number of firms adjust according to dN (р — 10) %D dt 4 (i) Derive the linear second-order differential equation implied by this model. (ii) Solve the second-order differential equation. (iii) Derive a system of differential equation to represent this information.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Consider a competitive market in which price adjusts to excess demand or supply and firms
enter and exit the industry if profits or losses are being made. Price adjusts to excess
demand according to
dp
0.5(qº – q$)
dt
%3D
Where qD
= 30 – 2p is the demand function, qs = 2N is the supply function, p is price, N is
%3D
the number of firms in the industry and a is the speed of adjustment coefficient. The
number of firms adjust according to
dN
(р — 10)
dt 4
(i)
Derive the linear second-order differential equation implied by this model.
(ii)
Solve the second-order differential equation.
(iii)
Derive a system of differential equation to represent this information.
(iv)
Solve the system.

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